Noise and Vibration Analysis: Signal Analysis and Experimental Procedures

by Anders Brandt

Overview

NOISE AND VIBRATION ANALYSIS

Complete guide to signal processing and modal analysis theory, with coverage of practical applications and a plethora of learning tools

Featuring numerous line diagrams and illustrations, the newly revised and updated Second Edition of Noise and Vibration Analysis is a comprehensive and practical guide that combines both signal processing and modal analysis theory with their practical application in noise and vibration analysis. This new edition has been updated with three new chapters covering experimental modal analysis, operational modal analysis, and practical vibration measurements.

Taking a practical learning approach, the text includes exercises that allow the content to be developed in an academic course framework or as supplementary material for private and further study, including multiple choice questions at the end of each chapter. An accompanying website hosts a MATLAB^® toolbox, additional problems and examples, and videos.

Written by a highly qualified author with significant experience in the field, Noise and Vibration Analysis covers topics such as:

• Dynamic signals and systems, covering periodic, random, and transient signals, RMS value and power, and the Continuous Fourier Transform
• Time data analysis, covering the sampling theorem, analog, digital, smoothing, and acoustic octave filters, time data differentiation, and FFT-based processing
• Statistics and random processes, covering expected value, errors in estimates, and probability distribution in random theory, and tests of normality and stationarity
• Fundamental mechanics, covering Newton’s laws, alternative quantities for describing motion, frequency response plot formats, and rotating mass

Noise and Vibration Analysis is an excellent resource for researchers and engineers from the automotive, aerospace, mechanical, or electronics industries who work with experimental or analytical vibration analysis and/or acoustics. The text is also valuable for graduate students enrolled in vibration analysis, experimental structural dynamics, or applied signal analysis courses.

Product Details

ISBN-13:	9781118962152
Publisher:	Wiley
Publication date:	06/27/2023
Sold by:	JOHN WILEY & SONS
Format:	eBook
Pages:	704
File size:	34 MB
Note:	This product may take a few minutes to download.

About the Author

Anders Brandt is a Professor and Head of the Department of Mechanical and Production Engineering at Aarhus University in Denmark. His research interests include vibration analysis, experimental and operational modal analysis, signal analysis, and system identification. He worked for 20 years in industry in Sweden and abroad, and gave over 250 short-courses on various topics in the field of vibration engineering. He is a member of the Society for Experimental Mechanics and is on the scientific committee for the International Operational Modal Analysis Conference.

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Table of Contents

About the Author xix

Preface xxi

Acknowledgments xxv

List of Abbreviations xxvii

Annotation xxix

1 Introduction 1

1.1 Noise and Vibration 1

1.2 Noise and Vibration Analysis 2

1.3 Application Areas 3

1.4 Analysis of Noise and Vibrations 4

1.5 Standards 5

1.6 Becoming a Noise and Vibration Analysis Expert 5

2 Dynamic Signals and Systems 9

2.1 Introduction 9

2.2 Periodic Signals 11

2.3 Random Signals 16

2.4 Transient Signals 17

2.5 RMS Value and Power 18

2.6 Linear Systems 19

2.7 The Continuous Fourier Transform 29

2.8 Chapter Summary 35

2.9 Problems 36

References 38

3 Time Data Analysis 39

3.1 Introduction to Discrete Signals 39

3.2 The Sampling Theorem 40

3.3 Filters 48

3.4 Time Series Analysis 57

3.5 Chapter Summary 66

3.6 Problems 67

References 68

4 Statistics and Random Processes 71

4.1 Introduction to the Use of Statistics 71

4.2 Random Theory 73

4.3 Statistical Methods 83

4.4 Quality Assessment of Measured Signals 91

4.5 Chapter Summary 94

4.6 Problems 95

References 96

5 Fundamental Mechanics 97

5.1 Newton’s Laws 97

5.2 The Single Degree-of-Freedom System (SDOF) 98

5.3 Alternative Quantities for Describing Motion 106

5.4 Frequency Response Plot Formats 108

5.5 Determining Natural Frequency and Damping Ratio 113

5.6 Rotating Mass 115

5.7 Some Comments on Damping 116

5.8 Models Based on SDOF Approximations 118

5.9 The Two Degree of Freedom System (2DOF) 121

5.10 The Tuned Damper 123

5.11 Chapter Summary 125

5.12 Problems 126

References 127

6 Modal Analysis Theory 129

6.1 Waves on a String 129

6.2 Matrix Formulations 131

6.3 Eigenvalues and Eigenvectors 132

6.4 Frequency Response of MDOF Systems 146

6.5 Free Decays 155

6.6 Chapter Summary 156

6.7 Problems 157

References 158

7 Transducers for Noise and Vibration Analysis 159

7.1 The Piezoelectric Effect 159

7.2 The Charge Amplifier 160

7.3 Transducers with Built-In Impedance Converters, “IEPE” 162

7.4 The Piezoelectric Accelerometer 165

7.5 The Piezoelectric Force Transducer 170

7.6 The Impedance Head 171

7.7 The Impulse Hammer 172

7.8 Accelerometer Calibration 173

7.9 Measurement Microphones 174

7.10 Microphone Calibration 175

7.11 The Geophone 175

7.12 MEMS-based Sensors 176

7.13 Shakers for Structure Excitation 177

7.14 Some Comments on Measurement Procedures 178

7.15 Problems 180

References 181

8 Frequency Analysis Theory 183

8.1 Periodic Signals – The Fourier Series 183

8.2 Spectra of Periodic Signals 185

8.3 Random Processes 187

8.4 Transient Signals 189

8.5 Interpretation of Spectra 189

8.6 Chapter Summary 191

8.7 Problems 192

References 193

9 Experimental Frequency Analysis 195

9.1 Frequency Analysis Principles 195

9.2 Octave and Third-Octave Band Spectra 197

9.3 The Discrete Fourier Transform (DFT) 198

9.4 Chapter Summary 224

9.5 Problems 225

References 226

10 Spectrum and Correlation Estimates Using the DFT 229

10.1 Averaging 229

10.2 Spectrum Estimators for Periodic Signals 230

10.3 Estimators for PSD and CSD 233

10.4 Estimators for Correlation Functions 250

10.5 Estimators for Transient Signals 258

10.6 A Signal Processing Framework for Spectrum and Correlation Estimation 260

10.7 Spectrum Estimation in Practice 262

10.8 Multichannel Spectral and Correlation Analysis 273

10.9 Chapter Summary 276

10.10 Problems 277

References 278

11 Measurement and Analysis Systems 281

11.1 Principal Design 282

11.2 Hardware for Noise and Vibration Analysis 283

11.3 FFT Analysis Software 295

11.4 Chapter Summary 299

11.5 Problems 300

Problems 300

References 301

12 Rotating Machinery Analysis 303

12.1 Vibrations in Rotating Machines 303

12.2 Understanding Time–Frequency Analysis 304

12.3 Rotational Speed Signals (Tachometer Signals) 306

12.4 RPM Maps 308

12.5 Smearing 310

12.6 Order Tracks 312

12.7 Synchronous Sampling 314

12.8 Averaging Rotation-Speed-Dependent Signals 317

12.9 Adding Change in RMS with Time 318

12.10 Parametric Methods 322

12.11 Chapter Summary 323

12.12 Problems 324

References 325

13 Single-input Frequency Response Measurements 327

13.1 Linear Systems 328

13.2 Determining Frequency Response Experimentally 328

13.3 Important Relationships for Linear Systems 333

13.4 The Coherence Function 333

13.5 Errors in Determining the Frequency Response 334

13.6 Coherent Output Power 339

13.7 The Coherence Function in Practice 340

13.8 Impact Excitation 342

13.9 Shaker Excitation 351

13.10 Examples of FRF Estimation – No Extraneous Noise 357

13.11 Example of FRF Estimation – With Output Noise 360

13.12 Examples of FRF Estimation – With Input and Output Noise 362

13.13 Chapter Summary 365

13.14 Problems 367

References 368

14 Multiple-Input Frequency Response Measurement 369

14.1 Multiple-Input Systems 369

14.2 Conditioned Input Signals 377

14.3 Bias and Random Errors for Multiple-Input Systems 384

14.4 Excitation Signals for MIMO Analysis 384

14.5 Data Synthesis and Simulation Examples 387

14.6 Real MIMO Data Case 393

14.7 Chapter Summary 396

14.8 Problems 397

References 398

15 Orthogonalization of Signals 401

15.1 Principal Components 401

15.2 Virtual Signals 410

15.3 Noise Source Identification (NSI) 417

15.4 Chapter Summary 422

15.5 Problems 423

References 424

16 Experimental Modal Analysis 425

16.1 Introduction to Experimental Modal Analysis 425

16.2 Experimental Setup 427

16.3 Introduction to Modal Parameter Extraction 437

16.4 SDOF Parameter Extraction 440

16.5 The Unified Matrix Polynomial Approach, UMPA 443

16.6 Time Versus Frequency Domain Parameter Extraction for EMA 452

16.7 Time Domain Parameter Extraction Methods 454

16.8 Frequency Domain Parameter Extraction Methods 470

16.9 Methods for Mode Shape Estimation and Scaling 480

16.10 Evaluating the Extracted Parameters 486

16.11 Chapter Summary 489

16.12 Problems 491

References 492

17 Operational Modal Analysis (OMA) 495

17.1 Principles for OMA 496

17.2 Data Acquisition Principles 497

17.3 OMA Modal Parameter Extraction for OMA 498

17.4 Scaling OMA Modal Models 508

17.5 Chapter Summary 512

17.6 Problems 514

References 514

18 Advanced Analysis Methods 517

18.1 Shock Response Spectrum 517

18.2 The Hilbert Transform 520

18.3 Cepstrum Analysis 527

18.4 The Envelope Spectrum 531

18.5 Creating Random Signals with Known Spectral Density 533

18.6 Identifying Harmonics in Noise 535

18.7 Harmonic Removal 539

18.8 Chapter Summary 542

18.9 Problems 543

References 544

19 Practical Vibration Measurements and Analysis 547

19.1 Introduction to a Plexiglas Plate 547

19.2 Forced Response Simulation 550

19.3 Spectra of Periodic Signals 556

19.4 Spectra of Random Signals 559

19.5 Data with Random and Periodic Content 561

19.6 Operational Deflection Shapes – ODS 567

19.7 Impact Excitation and FRF Estimation 572

19.8 Plexiglas EMA Example 578

19.9 Methods for EMA Modal Parameter Estimation, MPE 585

19.10 Conclusions of EMA MPE 599

19.11 OMA Examples 600

References 622

Appendix A Complex Numbers 625

Appendix B Logarithmic Diagrams 629

Appendix C Decibels 633

Appendix D Some Elementary Matrix Algebra 635

Appendix E Eigenvalues and the SVD 639

E.1 Eigenvalues and Complex Matrices 639

E.2 The Singular Value Decomposition (SVD) 640

Appendix F Organizations and Resources 643

Appendix G Checklist for Experimental Modal Analysis Testing 645

Bibliography 647

Index 659

What People are Saying About This

From the Publisher

"Here he presents the material in a form that can serve as a textbook or supplement for a graduate or undergraduate course or as a handbook for engineers or researchers who measure and analyze acoustic or vibration signals." (Booknews, 1 June 2011

Editorial Reviews

"Here he presents the material in a form that can serve as a textbook or supplement for a graduate or undergraduate course or as a handbook for engineers or researchers who measure and analyze acoustic or vibration signals." (Booknews, 1 June 2011

 

From the Publisher